Question

The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Answer 1

`z=(6.6-6.5)/((0.7)/(√(270)))=2.347`

The p value for this case would be given by"

`p_v =2*P(z>2.347)=0.0189`

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Explanation:

Information given

`\bar X=6.6` represent the sample mean

`s=√(0.49)= 0.7` represent the population deviation

`n=270` sample size

`\mu_o =6.5` represent the value that we want to test

`\alpha=0.1` represent the significance level

z would represent the statistic

`p_v` represent the p value for the test

Hypothesis to verify

We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:

Null hypothesis:
`\mu= 6.5`

Alternative hypothesis:
`\mu \\eq 6.5`

The statistic for this case is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

And replacing we got:

`z=(6.6-6.5)/((0.7)/(√(270)))=2.347`

The p value for this case would be given by"

`p_v =2*P(z>2.347)=0.0189`

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications